Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.83728%

Guaranteed chance to sample good point: 72.576832%

Results

19.0ms	39×	body	1280	valid
18.0ms	49×	body	640	valid
8.0ms	139×	body	80	valid
4.0ms	20×	body	320	valid
2.0ms	9×	body	320	invalid
1.0ms	4×	body	640	invalid
1.0ms	9×	body	160	valid
1.0ms	17×	body	80	invalid
1.0ms	5×	body	160	invalid
0.0ms	5×	body	80	nan

simplify114.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (7.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 9.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
4.9b	(pow (/ x (+ x y)) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 66

Calls

2 calls:

5.0ms	(/ x (+ x y))
6.0ms	(pow (/ x (+ x y)) x)

series22.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ x (+ x y))
17.0ms	(pow (/ x (+ x y)) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	451	502
1	2027	479
2	5002	474

prune115.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	8	73

Merged error: 1.1b

Counts

73 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.9b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`frac-times` `prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
15.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series107.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
21.0ms	(cbrt x)
27.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
38.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify93.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	977	1596
1	3500	1507
2	5002	1470

prune180.0ms

Filtered

88 candidates to 128 candidates (-45.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	128	8	136

Merged error: 0.4b

Counts

136 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.0b	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
1.9b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
15.3b	(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) x)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

193×	`cbrt-prod`
125×	`unpow-prod-down`
95×	`times-frac`
87×	`*-un-lft-identity`
69×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`cbrt-div`
26×	`add-exp-log`
18×	`associate-/r/`
13×	`flip3-+` `flip-+`
10×	`pow-exp`
9×	`pow-unpow` `distribute-lft-out`
8×	`frac-times`
7×	`pow1` `div-exp`
5×	`prod-exp`
4×	`associate-r/` `associate-l/` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-inv` `sqr-pow`
1×	`pow1/3`

Counts

4 → 185

Calls

4 calls:

1.0ms	(cbrt x)
16.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
17.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
11.0ms	(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) x)

series121.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
26.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
39.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
34.0ms	(pow (/ (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1536	3396
1	5001	3319

prune307.0ms

Filtered

156 candidates to 197 candidates (-26.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	197	8	205

Merged error: 0.4b

Counts

205 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.0b	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
1.9b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
15.6b	(pow (/ (cbrt (* (cbrt x) (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

193×	`cbrt-prod`
125×	`unpow-prod-down`
95×	`times-frac`
87×	`*-un-lft-identity`
69×	`add-sqr-sqrt` `add-cube-cbrt`
40×	`cbrt-div`
26×	`add-exp-log`
18×	`associate-/r/`
13×	`flip3-+` `flip-+`
10×	`pow-exp`
9×	`pow-unpow` `distribute-lft-out`
8×	`frac-times`
7×	`pow1` `div-exp`
5×	`prod-exp`
4×	`associate-r/` `associate-l/` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-inv` `sqr-pow`
1×	`pow1/3`

Counts

4 → 185

Calls

4 calls:

1.0ms	(cbrt x)
15.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
14.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
14.0ms	(pow (/ (cbrt (* (cbrt x) (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)

series120.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
27.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
34.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)
38.0ms	(pow (/ (cbrt (* (cbrt x) (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1528	3390
1	5001	3313

prune282.0ms

Filtered

156 candidates to 197 candidates (-26.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	197	8	205

Merged error: 0.4b

Counts

205 → 8

regimes122.0ms

Accuracy

30% (3.7b remaining)

Error of 5.1b against oracle of 1.4b and baseline of 6.7b

bsearch42.0ms

Steps

Iters	Range		Point
6	253.18644003778587	1807.8135826125513	278.2471189653204

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	50
1	31	50

end0.0ms

sample3.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.83728%

Guaranteed chance to sample good point: 72.576832%

Results

722.0ms	1447×	body	1280	valid
365.0ms	1217×	body	640	valid
249.0ms	4408×	body	80	valid
126.0ms	625×	body	320	valid
68.0ms	236×	body	640	invalid
43.0ms	203×	body	320	invalid
40.0ms	91×	body	1280	invalid
39.0ms	303×	body	160	valid
25.0ms	474×	body	80	invalid
13.0ms	108×	body	160	invalid
6.0ms	144×	body	80	nan

Details

sample1.1s

simplify114.0ms

prune6.0ms

localize6.0ms

rewrite13.0ms

series22.0ms

simplify56.0ms

prune115.0ms

localize16.0ms

rewrite32.0ms

series107.0ms

simplify93.0ms

prune180.0ms

localize30.0ms

rewrite56.0ms

series121.0ms

simplify63.0ms

prune307.0ms

localize33.0ms

rewrite55.0ms

series120.0ms

simplify61.0ms

prune282.0ms

regimes122.0ms

bsearch42.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling